Related papers: Texture and shape of two-dimensional domains of ne…
So far magnetic domain walls in one-dimensional structures have been described theoretically only in the cases of flat strips, or cylindrical structures with a compact cross-section, either square or disk. Here we describe an extended phase…
We present nonlinear dynamic equations for nematic and smectic $A$ liquid crystals in the presence of an alternating electric field and explain their derivation in detail. The local electric field acting in any liquid-crystalline system is…
We study the motion of a two-dimensional droplet on an inclined surface, under the action of gravity, using a diffuse interface model which allows for arbitrary equilibrium contact angles. The kinematics of motion is analysed by decomposing…
Ferroelectric nematic liquid crystals are polar fluids characterized by microscopic orientational ordering and macroscopic spontaneous polarizations. Within these fluids, walls that separate domains of different polarizations are…
This review introduces the elasticity theory of two-dimensional crystals and nematic liquid crystals on curved surfaces, the energetics of topological defects (disclinations, dislocations and pleats) in these ordered phases, and the…
Domain structure of a fluid ferroelectric nematic is dramatically different from the domain structure of solid ferroelectrics since it is not restricted by rectilinear crystallographic axes and planar surface facets. We demonstrate that…
In this paper we establish the uniformity property of a simplified Ericksen-Leslie system modelling the hydrodynamics of nematic liquid crystals on the two dimensional unit sphere $S^2$, namely the uniform convergence in $L^2$ to a steady…
Most genuine multi-sided surface representations depend on a 2D domain that enables a mapping between local parameters and global coordinates. The shape of this domain ranges from regular polygons to curved configurations, but the simple…
We consider a class of liquid crystal free-boundary problems for which both the equilibrium shape and internal configuration of a system must simultaneously be determined, for example in films with air- or fluid-liquid crystal interfaces…
In 3D nematic liquid crystals, disclination lines have a range of geometric structures. Locally, they may resemble $+1/2$ or $-1/2$ defects in 2D nematic phases, or they may have 3D twist. Here, we analyze the structure in terms of the…
Fine scale elastic structures are widespread in nature, for instances in plants or bones, whenever stiffness and low weight are required. These patterns frequently refine towards a Dirichlet boundary to ensure an effective load transfer.…
Liquid crystals establish a nearly unique combination of thermodynamic, hydrodynamic, and topological behavior. This poses a challenge to their theoretical understanding and modeling. The arena where these effects come together is the…
Linear defects such as dislocations and disclinations in ordered materials attract foreign particles since they replace strong elastic distortions at the defect cores. In this work, we explore the behavior of isotropic droplets nucleating…
Based on the observation that a particle motion in one dimension maps to a two-dimensional motion of a charged particle in a uniform magnetic field, constrained in the lowest Landau level, we formulate a system of one-dimen- sional…
Electronic nematic order has been reported in a rich landscape of materials, encompassing not only a range of intertwined correlated and topological phenomena, but also different underlying lattice symmetries. Motivated by these findings,…
Active drops refer to drops with the ability to self-migrate: these drops typically attain this ability by virtue of containing of active particles that derive energy from their environment and undergo directed motion inside the drops,…
We present a variety of structures formed by colloidal droplets at a nematic liquid crystal-air interface, where the elastic dipole-dipole, quadrupole-quadrupole, and dipole-quadrupole interactions are all essentially involved. The…
Periodic boundary conditions are a common theoretical and computational tool used to emulate effectively infinite domains. However, two-dimensional periodic domains are topologically distinct from the infinite plane, eliciting the question:…
The geometry and interactions between the constituents of a liquid crystal, which are responsible for inducing the partial order in the fluid, may locally favor an attempted phase that could not be realized in $\mathbb{R}^3$. While states…
We numerically study the effect of an active turbulent environment on a passive deformable droplet. The system is simulated using coupled hydrodynamic and nematodynamic equations for nematic liquid crystals with an active stress which is…